Question

Find dy if y=tan−1(2x ).

Answer 1

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Find dy/dx if $y=tan^{−1} (2x )$

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We know that differentiation of $tan^{-1} x=\frac{1}{1+x^2}$

$\sf \mapsto \frac{dy} {dx} =\frac{d(tan^{−1}2x)}{dx} \\\\\sf Applying~chain~rule: \\\\\sf =\frac{d(tan^{−1}2x)}{dx} = \frac{1}{1+(2x)^2}\frac{d(2x)}{dx} \\\\\sf \mapsto \frac{2}{1+4x^2}$